Non-Markovian spontaneous emission and photon localization in a atom-waveguide system

Waveguides can serve as a quantum channel for transporting photon qubits. Here we study the dynamics of a two-level atom in a single-mode waveguide, in particular, the spontaneous emission near the stop-off frequency of the waveguide. We found that even when the atomic transition frequency lies above the stop-off frequency of the waveguide, the emission is not complete due to the formation of a bound polariton state. Rabi oscillation due to splitting between the bound state and a resonance with finite lifetime is observed. This non-Markovian emission near the stop-off frequency reveals the strong coupling between the atom and the continuum. The trapped polariton makes the optical system behave like a cavity without mirror with the density-of-state singularity in a waveguide mimicking a discrete state in a cavity.